Question

If pressure $P$, velocity $V$ and time $T$ are taken as fundamental physical quantities, the dimensional formula of force is

• A. $[P{V}^2{T}^2]$
• B. $[P^{-1}{V}^2{T}^{-2}]$
• C. $[PV{T}^2]$
• D. $[P^{-1}V{T}^2]$

Answer 1

Answer: (A)

$\left[F\right]=\left[P^{\alpha }{V}^{\beta }{T}^{\gamma }\right]$
or $\left[M^1{L}^1{T}^{-2}\right]={\left[M^1{L}^{-1}{T}^{-2}\right]}^{\alpha }{\left[L{T}^{-1}\right]}^{\beta }{\left[T\right]}^{\gamma }$
or $\left[M^1{L}^1{T}^{-2}\right]=\left[M^{\alpha }{L}^{-\alpha +\beta }{T}^{-2\alpha -\beta +\gamma }\right]$
$\alpha =1;-\alpha +\beta =1;-2\alpha -\beta +\gamma =-2$
or $\beta =2;-2-2+\gamma =-2$
or $\gamma =2$
$\Rightarrow \left[F\right]=\left[P{V}^2{T}^2\right]$